Ejemplo de matriz 3x4 de rango 2
1. En la matriz A=
(
4
2
2
3
1
2
−1
1
6
3
5
0
)
MathType@MTEF@5@5@+=feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeaabaWaaqaafaaakeaadaqadaqaauaabiqacmaaaeaafaqabeGabaaabaGaaGinaaqaaiaaikdaaaaabaWaauIhaeaafaqabeGacaaabaGaaGOmaaqaaiaaiodaaeaacaaIXaaabaGaaGOmaaaaaaaabaqbaeGabiqaaaqaaiabgkHiTiaaigdaaeaacaaIXaaaaaqaaiaaiAdacaaMe8oabaqbaeaabeGaaaqaaiaaiodacaaMc8oabaGaaGynaiaaysW7aaaabaGaaGimaiaaykW7aaaacaGLOaGaayzkaaaaaa@4AB0@
,
la parte recuadrada proporciona un menor
M2 no nulo de orden 2.
2. Fijamos la fila 3 y orlamos M2 con la fila 3 y
la columna 1. Obtenemos el menor:
|
4
2
2
3
1
2
6
3
5
|=0
MathType@MTEF@5@5@+=feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeaabaWaaqaafaaakeaadaabdaqaauaabeqaciaaaeaafaqabeGabaaabaGaaGinaaqaaiaaikdaaaaabaWaauIhaeaafaqabeGacaaabaGaaGOmaaqaaiaaiodaaeaacaaIXaaabaGaaGOmaaaaaaaabaGaaGOnaaqaauaabeqabiaaaeaacaaIZaaabaGaaGynaaaaaaaacaGLhWUaayjcSdGaeyypa0JaaGimaaaa@44AB@
.
Como es nulo, continuamos orlando con la columna 4. Obtenemos el menor:
|
2
3
1
2
−1
1
3
5
0
|=0
MathType@MTEF@5@5@+=feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaaiaacaGaaeaabaWaaqaafaaakeaadaabdaqaauaabeqaciaaaeaadaqjEaqaauaabeqaciaaaeaacaaIYaaabaGaaG4maaqaaiaaigdaaeaacaaIYaaaaaaaaeaafaqaceGabaaabaGaeyOeI0IaaGymaaqaaiaaigdaaaaabaqbaeqabeGaaaqaaiaaiodaaeaacaaI1aaaaaqaaiaaykW7caaMc8UaaGimaaaaaiaawEa7caGLiWoacqGH9aqpcaaIWaaaaa@48A5@
.
Ya hemos agotado todas las columnas correspondientes a la fila 3. Tampoco hay
posibilidad de tomar otras filas. Concluimos que el rango de A es 2.